/ MATH 05 TEST REVIEW SHEET TO THE STUDENT: This Review Sheet gives you an outline of the topics covered on Test as well as practice problems. Answers are at the end of the Review Sheet. I. EXPRESSIONS A. Evaluate the epression For problems 4, evaluate each epression, if possible. Write answers as integers or simplified fractions.. when 4 s 5. 64 # -4 4. 4 when 4. 000 5. Customers are waiting in late at a department store. They arrive randomly at an average rate of per minute. If the clerk can wait on customers per minute, then the average time in minutes spent waiting in line if given by T for. #5 a) Complete the table n 0.5.5.9 T b) What happens to the waiting time as increases, but remains less than? 6. Find any values of the variable that make the epression undefined. a) c) a 5 b) d) 7 4 solution #6 n OLD TOPICS: For problems 7, evaluate each epression, if possible. Write answers as integers or simplified fractions. 7. 8. 9. bh when b and h 0 when 0.. 5 5 4. 5 #7 -
B. SIMPLIFY EXPRESSIONS For problems 8,. 4. 5. 4 4 8 8 a) state any values of the variable that make the rational epression undefined, then b) simplify each rational epression. 4 6. 4 4 7. b b 4 8. a a a a For problems 9 8, simplify each radical epression. Do not give a decimal answer. Assume all variables are positive. 9. 0. 80... 49 8 5 y b 90 0 # - 5 #0-4. 5. 4 64 y 6 8a 6. 7 7. 8. 5 t 6 #6-8 #4-7 OLD TOPICS: For problems 9, simplify each epression. 9. 0. (4 ) ( ) 5 4 8 ( a b )( a b ) C. OPERATIONS ON EXPRESSIONS. 6. 4( ) () #9 - For problems 44, perform the indicated operation on the rational epressions. Simplify to lowest terms. Leave answers in factored form.. 4 6 9 6 55 4. 9 5 5. 5 6 6 # - 5 6. 7. 8. u u u 6 u u 4 50 #6-8
b 5b 9. b b b b m m 40. m m 4. #9-4 4. 4 4 4. 9 4n n 44. n n #4, 4 #44 For problems 45 5, perform the indicated operations on the radical epressions. Simplify the epressions by factoring out the largest perfect square factors. Assume that all variables are positive. 45. 5 5 46. a a 47. 5 48. 4 49. 5 8 8 50. 4 7 #47, 49-5 5. 5. 5. 75 6 6 5 8ab ab #5, 5 OLD TOPICS: For problems 54 58, multiply and simplify each epression. 54. ( 4) 55. ()( 5) 56. ( a)( a ) 57. 8 5 58. ( )( 4) #55-58 For problems 59 65, factor the epressions completely, or write prime. 59. 60. 6. 6. n n 6 6 5 64 #59-6 6. b 8b 8 64. t 8t 48t 65. 0 4 #64-66 66. Is it true that 4 6? Eplain why or why not. For problems 67 68, simplify the eponent epressions by remove all negative and zero eponents. Assume all epressions are defined. 67. a b a b 68. 6 8y #67-68
II. SOLVING EQUATIONS A. SOLVING RATIONAL EQUATIONS For problems 69 77, solve each of the following rational equations and find any values of the variable that make the epression undefined. 69. 70. 7. 7. 7. 4 5 5 0 0 0 5 B. SOLVING RADICAL EQUATIONS 74. 4 4 75. 8 5 5 76. 4 77. For problems 78 8, solve and check each of the following radical equations 78. 4 4 79. 6 80. 6 C. SOLVING WITH TECHNOLOGY 8. z 6 z 8. 4 y y For problems 8 89, use your graphing calculator to solve the equations graphically or numerically: 8. Solve graphically:. For your work, sketch a graph of each side of the equation on the same coordinate aes. Circle and clearly label the solution(s) separate from the graph. 84. Solve numerically: #69, 70, 7 #79. For your work, provide a copy of the table use to solve, with the solution row(s) #8 #7, 74 #76, 77 #8 #84 clearly identified and include a row above and below to solution separate from the table. 85. Solve graphically: 4. For your work, sketch a graph of each side of the equation on the same coordinate aes. Circle and clearly label the solution(s) separate from the graph. Use algebra to solve the equation. Show work.
86. Solve graphically, if possible: 5. For your work, sketch a graph of each side of the equation on the same coordinate aes. Circle and clearly label the solution(s) separate from the graph. 87. Solve graphically:. For your work, sketch a graph of each side of the equation on the same coordinate aes. Circle and clearly label the solution(s) separate from the graph. Use algebra to solve the equation. Show work. 88. Solve numerically: 6. For your work, provide a copy of the table used to solve, with the solution row(s) clearly identified and include a row above and below to solution. #88 #86 89. Solve graphically: 5, by converting to standard from and graphing the resulting polynomial. For your work, sketch a graph of the equation, then circle and clearly label the solution(s). Use algebra to solve the equation. Show work. OLD TOPICS For problems 90 96, solve the following equations or inequality. 90. 5 0 9. 4 9. 7 5 0 4 9. 75 0 #90-9 6 5 7 5 94. 95. 96. 5( ) 6. Also graph the solution set on a number line and epress in interval notation. #9-95 #96 For problems 97 00, solve the systems of equations by either the elimination or substitutions method. 97. 98. 5 5y 5 y 7 7y 5y 0 III. FORMULAS 99. 00. y y 6 y9 y 4 #99 #00 For problems 0 07, solve for the indicated variable. Assume there are no zero denominators.
0. 0. for d 5 d V r h for h 0. P 6a b for b 04. for c a b c #0, 0, 04 at 05. R for T T r 06. for R. T R r D 07. T for D 4V #05-07 08. Use the distance formula (, 4) and (5,0) d ( ) ( y y ) to find the distance between IV. APPLICATION PROBLEMS A. RATIONAL APPLICATION: For problems 09 4, set up and solve a rational equation to find the indicated value. Round to the nearest tenth. 09. It will take Yansin 8 hours to paint a house alone. #09 It will take Jared 0 hours to paint the same house alone. How many hours will it take them working together? 0. It will take Sarita 4 hours to prepare a party. It will take Jasmine 6 hours to prepare the same party. How many hours will it take them working together?. (Optional ask your instructor) An airplane can travel 80 miles into the wind in the same time that it can travel 40 miles with the wind. If the wind speed is 0 miles per hour, find the speed without any wind. #. (Optional ask your instructor) A boat can travel 4 miles upstream in the same time that it can travel 86 miles downstream. If the speed of the current is 6 miles per hour, find the speed of the boat without current. B. QUADRATIC APPLICATION. A baseball is hit into the air and its height h in feet after t seconds can be calculated by h 6t 96t. a) What is the height of the baseball when it is first hit? b) What is the maimum height of the baseball? OLD TOPICS # 4. A solution contains 5% salt. How much pure water should be added to 40 ounces of the solution to dilute it to a % solution?
5. A riverboat takes 8 hours to travel 64 miles downstream and 6 hours for the return trip. What is the speed of the current and the speed of the riverboat in still water? #4, 5 6. Monthly average high temperature in degrees Fahrenheit in Columbus Ohio can be approimated by the polynomial F.466 0.5 9, where = corresponds to January, = to February, and so on. Use your graphing calculator to make a table using integer inputs = to =. What is the average high in May? 7. The elevation of Mt. Everest is 8850 meters. Change this elevation to feet. Write your answer in scientific notation. meter = 9.7 inches V. GRAPHING 8. For the quadratic equation y 4, a) find the y intercept b) find the intercept c) find the ais of symmetry d) find the verte e) Use a graphing calculator to check your results 9. For the quadratic equation y 6 7, a) Find the y- intercept b) find the -intercept c) find the ais of symmetry d) find the verte e) Use a graphing calculator to check your results #8 a) - b) #8 b) - e) OLD TOPICS 0. On graph paper, draw a line with a slope of and passing through (, ). Label each ais and three other points. Find the equation of the line. #0 part. Graph y 6 #0 part. Find the equation of a line with a zero slope which passes through (4, ). Graph this equation.. Find the equation of the line passing through (, ) and (, 5). Graph this equation and label the y-intercept on the graph. 4. Write the point slope equation of the line passing through (5, -4) with slope # # m #4
ANSWERS TO PROBLEMS MATH 05 TEST REVIEW SHEET I. Epressions A. Evaluating Epressions. 4 / 9. Undefined. 8 4. 0 5. a) Table: X 0.5.5.9 T / 0 b) T increases greatly 6. a) all real numbers ecept 5 b) all real numbers ecept 4 and - (,4 ) c) a 0 d) all real numbers 7. 5 8. 0 9. 9 0. 8. 5 6 = 565. 5/9 B. Simplifying Epression., ; 4. 4; 5. 8 8; 8 6. ; 7. b, ; b 8. a, ; a a 9. 7/9 0. 4 5. 4b. y y. 4. 8 y 5. a 7 6. 7. 5 8. t/4 9. 6 9 0. ab.. C. Operations on Epressions. ( ) 4. 5. 6 6 6. 7. u 8. ( ) 5 9. 4 b 40. m 4. 6 ( )( ) 4. ( ) 4. ( )( ) 44. 7n n (n)( n) 45. 5 46. 5 a 47. 6 48. 49. 50. 5. 5 5. 6/5 5. Old Topics: 54. 8 6 55. 6 0 56. a 9 57. 5 58. 7 4 59. ( 4)( ) 60. (n)( n 6) 6. ()( 5) 6. ( 8)( 8) 6. ( b ) 64. t( t )( t 8) 65. ( )( )
66. It is false. Missing middle term. 67. ab 68. 6y 9 II. Solving Equations A. Solving Rational Equations 69. 0,, = 9 70. 0, = 7. 5, =, = 7 7. = / 7., = 5 74. 4, = / 75. = 60 76., no solution 77., = 0, = / B. Solving Radical Equations 78. = 6 79. = 80. -, = 8. 4, = 9 8. 0, = C. Solving with Technology 8. s: =0 and = 86. There is no solution. The graphs do not intersect. 87. : = 88. Numerically: s: = 7, 9 Y= 6 8 5 9 0 0 7 Y= 6 6 5 7 0 8 7 84. s: = and = Y= / Y = 0 Und Y= / Y = 0 / 85. : =7 / 5.6667 89. s: = 0.5 and = Old Topics 90. 5 9. 0,, 9. 5, / 9. 0, 5, 5 94. 95.
96. < (, ) 97. (4, 5) 98. (5,) 99. ( 4, ) 00. Infinitely many solutions III. Formulas 0. d=0/ V 0. h r P 0. b a ab 04. c a b RT 05. T a 06. R=T r + r 07. D=4VT 08. 85 IV. Application A. Rational Applications 09. Let = # hours it will take them working together ; 4.4 hours to finish 8 0 0. Let = # of hours it will take them working together ; =.4 hours working together 4 6. 80 40 ; =00 mph 0 0. 4 86 ; = 5mph 6 6. a) feet initially (t=0); b) ma height is the y-coord. of verte47 ft. 4. 6.667 gallons of water is needed to dilute it 5. Current: mph; Riverboat: 6mph 6. Complete table for to.466 0.5 9 7.784 4.66 56.556 4 66.544 5 7.6 40.896 The average high in May (=5) is 7.6 degrees 7. 9.7in ft 4 8850m 905.4 ft.90 0 ft m in V. Graphing 8. a) (0, ) c = ; b) (,0) and(6,0) ; c) = d) (, 6) 9. a) (0, 7) c = 7; b) ( 7,0) and (,0); c) = - d) (, 6) 0. y ( ) y. Graph of. y = y = - (, ) y 6 y. y = 4 4. y 4 ( 5) y y (, 5) y = -4 (4, -)